Paramagnetic Coupling

If a material contains a localised unpaired electron (e.g. on an ion) this electron can cause an additional magnetic field at the nucleus. The interaction Hamiltonian between the nucleus (I) and the electron (S) can be generally written as 

The coupling tensor (P) to the paramagnetic ion produces two main sources of additional field. One is the Fermi contact or hyperfine interaction. The general form of the contact interaction produces a Hamiltonian 

The mean electron moment given by Eq. 2.69 will only be parallel to Bq if g is isotropic. If the nucleus being observed is not the ion with the initial unpaired electron, spin s-orbital polarisation can still be induced through effects transferred via the chemical bond, in which case it is called the transferred hyperfine interaction. This effect can still be strong although it will decrease rapidly as the number of intermediate bonds 

In paramagnetic systems the Fermi contact term is expected to dominate. However in addition there is also the possibility of a through-space dipolar effect. The shift caused hy the trace of this tensor interaction is often called the pseudocontact effect, which for a lanthanide ion is given by 

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Mavankal G, McCain DC, Bricker TM. Effects of chloride on paramagnetic coupling of manganese in calcium chloride-washed Photosystem II preparations. FEBS Lett 1986 202 235-239. 

Mounting electrodes in a bioreactor is costly, and there is an additional contamination risk for sensitive cell cultures. Some other sensors of prac ticai importance are those for dissolved oxygen and for dissolved carbon dioxide. The analysis of gas exiting from a bioreactor with an infrared unit that detects carbon dioxide or a paramagnetic unit that detects oxygen (after carbon dioxide removal) has been replaced by mass spec trophotometry. Gas chromatographic procedures coupled with a mass spectrophotometer will detect 1 the volatile components. 

For the paramagnetic case the expre.ssion for the photo current in Eq. (2) can be simplified to a concentration weighted sum over the products of the K-resolved partial density of states (DOS) ri (F) and a corresponding matrix element that smoothly varies with energy [13]. This simple interpretation of the XPS-spectra essentially also holds for the more complex spin-resolved ca e in the presence of spin-orbit coupling as studied here. 

After the discovery of the oscillatory magnetic interlayer coupling between ferromagnetic films separated by a paramagnetic spacer these sandwiched systems have been a subject of intense research. There have been many attempts to explain the magnetic interlayer coupling and a great number of theoretical and experimental studies have been performed . ... 

The complex ion (Figure 2.32) contains Rh2 bound cis to two phosphorus atoms (2.216 A) and more distantly to four oxygens (2.201—2.398 A), exhibiting a distortion ascribed to the Jahn-Teller effect it is paramagnetic (fi = 1.80 fiB) and exhibits an ESR spectrum (Figure 2.33) showing rhodium hyperfine coupling as the doublet for g. ... 

Desulforubidin was found in strains of the Desulfomicrobium genus and has been described as the sulfite reductase of this genus. The subunit composition and molecular mass are similar to what was observed for desulfoviridin. However, in desulforubidin all sirohydrochlorins are metalated as proved by Mossbauer spectroscopy (152). The as-isolated protein contains four [4Fe-4S] clusters two of them are exchange-coupled to two paramagnetic sirohemes. 

A resonant Orbach process occurs when the energy of the coupled vibrational modes is equal to the energy A of the first excited level of the paramagnetic center. This leads to the temperature dependence 1/Ti oc (exp(A/ BT) 1) expi- /ksT) when ksT < A. 

The strength of the coupling of the paramagnetic center to its surroundings, which is determined by the orbital part of the... 

The intrinsic relaxation rate of a paramagnetic center can he enhanced hy spin—spin coupling with a nearhy fast-relaxing species. 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

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